Distributed adaptive Gaussian mean estimation with unknown variance: Interactive protocol helps adaptation
研究了通信约束下未知方差高斯均值的分布式估计，推导了不同协议下自适应率最优估计的必要和充分通信成本，发现交互协议比独立协议更节省通信成本。
Distributed estimation of a Gaussian mean with unknown variance under communication constraints is studied. Necessary and sufficient communication costs under different types of distributed protocols are derived for any estimator that is adaptively rate-optimal over a range of possible values for the variance. Communication-efficient and statistically optimal procedures are developed. The analysis reveals an interesting and important distinction among different types of distributed protocols: compared to the independent protocols, interactive protocols such as the sequential and blackboard protocols require less communication costs for rate-optimal adaptive Gaussian mean estimation. The lower bound techniques developed in the present paper are novel and can be of independent interest.